1 // SPDX-License-Identifier: GPL-2.0
2 /*
3 * Functions for incremental mean and variance.
4 *
5 * This program is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 as published by
7 * the Free Software Foundation.
8 *
9 * This program is distributed in the hope that it will be useful, but WITHOUT
10 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
11 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
12 * more details.
13 *
14 * Copyright © 2022 Daniel B. Hill
15 *
16 * Author: Daniel B. Hill <daniel@gluo.nz>
17 *
18 * Description:
19 *
20 * This is includes some incremental algorithms for mean and variance calculation
21 *
22 * Derived from the paper: https://fanf2.user.srcf.net/hermes/doc/antiforgery/stats.pdf
23 *
24 * Create a struct and if it's the weighted variant set the w field (weight = 2^k).
25 *
26 * Use mean_and_variance[_weighted]_update() on the struct to update it's state.
27 *
28 * Use the mean_and_variance[_weighted]_get_* functions to calculate the mean and variance, some computation
29 * is deferred to these functions for performance reasons.
30 *
31 * see lib/math/mean_and_variance_test.c for examples of usage.
32 *
33 * DO NOT access the mean and variance fields of the weighted variants directly.
34 * DO NOT change the weight after calling update.
35 */
36
37 #include <linux/bug.h>
38 #include <linux/compiler.h>
39 #include <linux/export.h>
40 #include <linux/limits.h>
41 #include <linux/math.h>
42 #include <linux/math64.h>
43 #include <linux/module.h>
44
45 #include "mean_and_variance.h"
46
47 u128_u u128_div(u128_u n, u64 d)
48 {
49 u128_u r;
50 u64 rem;
51 u64 hi = u128_hi(n);
52 u64 lo = u128_lo(n);
53 u64 h = hi & ((u64) U32_MAX << 32);
54 u64 l = (hi & (u64) U32_MAX) << 32;
55
56 r = u128_shl(u64_to_u128(div64_u64_rem(h, d, &rem)), 64);
57 r = u128_add(r, u128_shl(u64_to_u128(div64_u64_rem(l + (rem << 32), d, &rem)), 32));
58 r = u128_add(r, u64_to_u128(div64_u64_rem(lo + (rem << 32), d, &rem)));
59 return r;
60 }
61 EXPORT_SYMBOL_GPL(u128_div);
62
63 /**
64 * mean_and_variance_get_mean() - get mean from @s
65 * @s: mean and variance number of samples and their sums
66 */
67 s64 mean_and_variance_get_mean(struct mean_and_variance s)
68 {
69 return s.n ? div64_u64(s.sum, s.n) : 0;
70 }
71 EXPORT_SYMBOL_GPL(mean_and_variance_get_mean);
72
73 /**
74 * mean_and_variance_get_variance() - get variance from @s1
75 * @s1: mean and variance number of samples and sums
76 *
77 * see linked pdf equation 12.
78 */
79 u64 mean_and_variance_get_variance(struct mean_and_variance s1)
80 {
81 if (s1.n) {
82 u128_u s2 = u128_div(s1.sum_squares, s1.n);
83 u64 s3 = abs(mean_and_variance_get_mean(s1));
84
85 return u128_lo(u128_sub(s2, u128_square(s3)));
86 } else {
87 return 0;
88 }
89 }
90 EXPORT_SYMBOL_GPL(mean_and_variance_get_variance);
91
92 /**
93 * mean_and_variance_get_stddev() - get standard deviation from @s
94 * @s: mean and variance number of samples and their sums
95 */
96 u32 mean_and_variance_get_stddev(struct mean_and_variance s)
97 {
98 return int_sqrt64(mean_and_variance_get_variance(s));
99 }
100 EXPORT_SYMBOL_GPL(mean_and_variance_get_stddev);
101
102 /**
103 * mean_and_variance_weighted_update() - exponentially weighted variant of mean_and_variance_update()
104 * @s: mean and variance number of samples and their sums
105 * @x: new value to include in the &mean_and_variance_weighted
106 * @initted: caller must track whether this is the first use or not
107 * @weight: ewma weight
108 *
109 * see linked pdf: function derived from equations 140-143 where alpha = 2^w.
110 * values are stored bitshifted for performance and added precision.
111 */
112 void mean_and_variance_weighted_update(struct mean_and_variance_weighted *s,
113 s64 x, bool initted, u8 weight)
114 {
115 // previous weighted variance.
116 u8 w = weight;
117 u64 var_w0 = s->variance;
118 // new value weighted.
119 s64 x_w = x << w;
120 s64 diff_w = x_w - s->mean;
121 s64 diff = fast_divpow2(diff_w, w);
122 // new mean weighted.
123 s64 u_w1 = s->mean + diff;
124
125 if (!initted) {
126 s->mean = x_w;
127 s->variance = 0;
128 } else {
129 s->mean = u_w1;
130 s->variance = ((var_w0 << w) - var_w0 + ((diff_w * (x_w - u_w1)) >> w)) >> w;
131 }
132 }
133 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_update);
134
135 /**
136 * mean_and_variance_weighted_get_mean() - get mean from @s
137 * @s: mean and variance number of samples and their sums
138 * @weight: ewma weight
139 */
140 s64 mean_and_variance_weighted_get_mean(struct mean_and_variance_weighted s,
141 u8 weight)
142 {
143 return fast_divpow2(s.mean, weight);
144 }
145 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_mean);
146
147 /**
148 * mean_and_variance_weighted_get_variance() -- get variance from @s
149 * @s: mean and variance number of samples and their sums
150 * @weight: ewma weight
151 */
152 u64 mean_and_variance_weighted_get_variance(struct mean_and_variance_weighted s,
153 u8 weight)
154 {
155 // always positive don't need fast divpow2
156 return s.variance >> weight;
157 }
158 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_variance);
159
160 /**
161 * mean_and_variance_weighted_get_stddev() - get standard deviation from @s
162 * @s: mean and variance number of samples and their sums
163 * @weight: ewma weight
164 */
165 u32 mean_and_variance_weighted_get_stddev(struct mean_and_variance_weighted s,
166 u8 weight)
167 {
168 return int_sqrt64(mean_and_variance_weighted_get_variance(s, weight));
169 }
170 EXPORT_SYMBOL_GPL(mean_and_variance_weighted_get_stddev);
171
172 MODULE_AUTHOR("Daniel B. Hill");
173 MODULE_LICENSE("GPL");
174
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